scholarly journals Multiscale analysis of Galactic dust emission using complex wavelet transforms – I. Separation of Gaussian and non-Gaussian fluctuations in Herschel observations

2014 ◽  
Vol 440 (3) ◽  
pp. 2726-2741 ◽  
Author(s):  
J.-F. Robitaille ◽  
G. Joncas ◽  
M.-A. Miville-Deschênes
Keyword(s):  
Wavelet Transforms ◽  
Multiscale Analysis ◽  
Dust Emission ◽  
Gaussian Fluctuations ◽  
Complex Wavelet ◽  
Non Gaussian

Signal quantitative analysis using customizable perfect-translation-invariant complex wavelet functions

2014 ◽  
Vol 12 (04) ◽  
pp. 1460010 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Quantitative Analysis ◽  
Frequency Band ◽  
Wavelet Transforms ◽  
Wavelet Coefficient ◽  
Discrete Wavelet ◽  
Digital Signals ◽  
Orthonormal Wavelet ◽  
Translation Invariant ◽  
Fast Calculation ◽  
Complex Wavelet

In this paper, we introduce several methods of signal quantitative analysis using the perfect-translation-invariant complex wavelet functions (PTI complex wavelet functions), which are used in our proposed perfect-translation-invariant complex discrete wavelet transforms (PTI CDWTs) and can be designed by customization. First, using PTI complex wavelet functions, we define the continuous wavelet coefficient (CWC). Next, using orthonormal wavelet functions in the classical Hardy space, we analyze the CWC, and show that, using a CWC, we can measure the energy of a customizable frequency band, and additionally, using numbers of CWCs, we can measure the energy of the whole frequency band. Next, we introduce the fast calculation method of CWCs and show the applicability of the PTI CDWTs to digital signals. Based on them, we introduce some examples of signal quantitative analysis, including the methods to obtain instantaneous amplitude, instantaneous phase and instantaneous frequency. Additionally, we introduce the energy measurement of the whole frequency band using the PTI DT-CDWT, which is one of our proposed PTI CDWTs.

scholarly journals The holographic spacetime model of cosmology

2018 ◽  
Vol 27 (14) ◽  
pp. 1846005 ◽  
Author(s):  
Tom Banks ◽  
W. Fischler
Keyword(s):  
Dark Matter ◽  
Gravitational Waves ◽  
Structure Formation ◽  
Big Bang ◽  
Baryon Asymmetry ◽  
Gaussian Fluctuations ◽  
Primordial Gravitational Waves ◽  
Conventional Models ◽  
Non Gaussian ◽  
The Big Bang

This essay outlines the Holographic Spacetime (HST) theory of cosmology and its relation to conventional theories of inflation. The predictions of the theory are compatible with observations, and one must hope for data on primordial gravitational waves or non-Gaussian fluctuations to distinguish it from conventional models. The model predicts an early era of structure formation, prior to the Big Bang. Understanding the fate of those structures requires complicated simulations that have not yet been done. The result of those calculations might falsify the model, or might provide a very economical framework for explaining dark matter and the generation of the baryon asymmetry.

Neural Networks and HOS for Power Quality Evaluation

2011 ◽  
pp. 1226-1231
Author(s):  
Juan J. González De la Rosa ◽  
Carlos G. Puntonet ◽  
A. Moreno-Muñoz
Keyword(s):  
Signal Processing ◽  
Power Quality ◽  
Wavelet Transforms ◽  
Learning Rule ◽  
Higher Order ◽  
Second Order ◽  
Voltage Waveform ◽  
Long Duration ◽  
Non Linear Load ◽  
Non Gaussian

Power quality (PQ) event detection and classification is gaining importance due to worldwide use of delicate electronic devices. Things like lightning, large switching loads, non-linear load stresses, inadequate or incorrect wiring and grounding or accidents involving electric lines, can create problems to sensitive equipment, if it is designed to operate within narrow voltage limits, or if it does not incorporate the capability of filtering fluctuations in the electrical supply (Gerek et. al., 2006; Moreno et. al., 2006). The solution for a PQ problem implies the acquisition and monitoring of long data records from the energy distribution system, along with an automated detection and classification strategy which allows identify the cause of these voltage anomalies. Signal processing tools have been widely used for this purpose, and are mainly based in spectral analysis and wavelet transforms. These second-order methods, the most familiar to the scientific community, are based on the independence of the spectral components and evolution of the spectrum in the time domain. Other tools are threshold-based algorithms, linear classifiers and Bayesian networks. The goal of the signal processing analysis is to get a feature vector from the data record under study, which constitute the input to the computational intelligence modulus, which has the task of classification. Some recent works bring a different strategy, based in higher-order statistics (HOS), in dealing with the analysis of transients within PQ analysis (Gerek et. al., 2006; Moreno et. al., 2006) and other fields of Science (De la Rosa et. al., 2004, 2005, 2007). Without perturbation, the 50-Hz of the voltage waveform exhibits a Gaussian behaviour. Deviations from Gaussianity can be detected and characterized via HOS. Non-Gaussian processes need third and fourth order statistical characterization in order to be recognized. In order words, second-order moments and cumulants could be not capable of differentiate non-Gaussian events. The situation described matches the problem of differentiating between a transient of long duration named fault (within a signal period), and a short duration transient (25 per cent of a cycle). This one could also bring the 50-Hz voltage to zero instantly and, generally affects the sinusoid dramatically. By the contrary, the long-duration transient could be considered as a modulating signal (the 50-Hz signal is the carrier). These transients are intrinsically non-stationary, so it is necessary a battery of observations (sample registers) to obtain a reliable characterization. The main contribution of this work consists of the application of higher-order central cumulants to characterize PQ events, along with the use of a competitive layer as the classification tool. Results reveal that two different clusters, associated to both types of transients, can be recognized in the 2D graph. The successful results convey the idea that the physical underlying processes associated to the analyzed transients, generate different types of deviations from the typical effects that the noise cause in the 50-Hz sinusoid voltage waveform. The paper is organized as follows: Section on higher-order cumulants summarizes the main equations of the cumulants used in the paper. Then, we recall the competitive layer’s foundations, along with the Kohonen learning rule. The experience is described then, and the conclusions are drawn.

Generation of non-Gaussian fluctuations during chaotic inflation

1991 ◽  
Vol 43 (2) ◽  
pp. 362-368 ◽  
Author(s):  
Insu Yi ◽  
Ethan T. Vishniac ◽  
Shin Mineshige
Keyword(s):  
Gaussian Fluctuations ◽  
Non Gaussian ◽  
Chaotic Inflation

scholarly journals Statistical Patterns of Transmission Losses of Low-Frequency Sound in Shallow Sea Waveguides with Gaussian and Non-Gaussian Fluctuations

2019 ◽  
Vol 9 (9) ◽  
pp. 1841
Author(s):  
Fengqin Zhu ◽  
Oleg E. Gulin ◽  
Igor O. Yaroshchuk
Keyword(s):  
Acoustic Field ◽  
Speed Of Sound ◽  
Transmission Loss ◽  
Low Frequency ◽  
Local Mode ◽  
Average Intensity ◽  
Slowing Down ◽  
Gaussian Fluctuations ◽  
Mode Method ◽  
Non Gaussian

Based on the local mode method, the problem of the average intensity (transmission loss) behavior in shallow waveguides with losses in the bottom and fluctuations of the speed of sound in water is considered. It was previously shown that the presence in a waveguide with absorbing penetrable bottom of 2D random inhomogeneities of the speed of sound leads to the appearance of strong fluctuations in the acoustic field already at relatively small distances from the sound source. One of the most important and interesting manifestations of this is the slowing down of the average intensity of the acoustic field compared with a waveguide, which has no such random inhomogeneities of the speed of sound. This paper presents the results of a numerical analysis of the decay of the average field intensity in the presence of both Gaussian and non-Gaussian fluctuations in the speed of sound. It is shown that non-Gaussian fluctuations do not fundamentally change the conclusion about reducing losses during the propagation of a sound signal but can enhance this effect.

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